Zero-conductance resonances and spin filtering effects in ring conductors subject to Rashba coupling

We investigate the effect of Rashba spin-orbit coupling and of a tunnel barrier on the zero-conductance resonances appearing in a one-dimensional conducting Aharonov-Bohm (AB) ring symmetrically coupled to two leads. The transmission function of the corresponding one-electron problem is derived within the scattering matrix approach and analyzed in the complex energy plane with focus on the role of the tunnel barrier strength on the zero-pole structure characteristic of transmission (anti)resonances. The lifting of the real conductance zeros is related to the breaking of the spin-reversal symmetry and time-reversal symmetry of Aharonov-Casher and AB rings, as well as to rotational symmetry breaking in the presence of a tunnel barrier. We show that the polarization direction of transmitted electrons can be controlled via the tunnel barrier strength and discuss a possible spin-filtering design in one-dimensional rings with tunable spin-orbit interaction.